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Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations

Author

Listed:
  • Syahmi Afandi Sariman

    (Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia)

  • Ishak Hashim

    (Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia)

  • Faieza Samat

    (GENIUS@Pintar National Gifted Centre, Universiti Kebangsaan Malaysia, Bangi Selangor 43600, Malaysia)

  • Mohammed Alshbool

    (Department of Applied Mathematics, Abu Dhabi University, Abu Dhabi, P.O. Box 59911, United Arab Emirates)

Abstract

In this study, we propose an extension of the modified Newton-Househölder methods to find multiple roots with unknown multiplicity of nonlinear equations. With four functional evaluations per iteration, the proposed method achieves an optimal eighth order of convergence. The higher the convergence order, the quicker we get to the root with a high accuracy. The numerical examples have shown that this scheme can compete with the existing methods. This scheme is also stable across all of the functions tested based on the graphical basins of attraction.

Suggested Citation

  • Syahmi Afandi Sariman & Ishak Hashim & Faieza Samat & Mohammed Alshbool, 2021. "Modification of Newton-Househölder Method for Determining Multiple Roots of Unknown Multiplicity of Nonlinear Equations," Mathematics, MDPI, vol. 9(9), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1020-:d:547091
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    References listed on IDEAS

    as
    1. Sharma, Rajni & Bahl, Ashu, 2015. "A sixth order transformation method for finding multiple roots of nonlinear equations and basin attractors for various methods," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 105-117.
    2. Moin-ud-Din Junjua & Fiza Zafar & Nusrat Yasmin, 2019. "Optimal Derivative-Free Root Finding Methods Based on Inverse Interpolation," Mathematics, MDPI, vol. 7(2), pages 1-10, February.
    3. Sharifi, Somayeh & Salimi, Mehdi & Siegmund, Stefan & Lotfi, Taher, 2016. "A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 69-90.
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